Use the Time::JulianDay module (part of the Time-modules bundle available from CPAN.)
Before you immerse yourself too deeply in this, be sure to verify that it is the Julian Day you really want. Are you interested in a way of getting serial days so that you just can tell how many days they are apart or so that you can do also other date arithmetic? If you are interested in performing date arithmetic, this can be done using modules Date::Manip or Date::Calc.
There is too many details and much confusion on this issue to cover in this FAQ, but the term is applied (correctly) to a calendar now supplanted by the Gregorian Calendar, with the Julian Calendar failing to adjust properly for leap years on centennial years (among other annoyances). The term is also used (incorrectly) to mean: [1] days in the Gregorian Calendar; and [2] days since a particular starting time or `epoch', usually 1970 in the Unix world and 1980 in the MS-DOS/Windows world. If you find that it is not the first meaning that you really want, then check out the Date::Manip and Date::Calc modules. (Thanks to David Cassell for most of this text.)